> As a relatively inexperienced user of Mathematica, could
> someone inform me how to get a closed-form expression--in
> terms of elementary functions if possible--for the inverse
> of the function
>
> f(x) = x^x
>
> Since the function is one-to-one over its domain, it does
> have a mathematical inverse.
x^x is not one-to-one on (0,inf). A graph over the interval (0,1)
clearly fails the horizontal line test.
Even on a restricted interval where it is one-to-one, there is no
reason to believe one can write a closed-form expression (i.e.
elementary function) for the inverse. I strongly suspect that is not
possible in this case.
Richard Mercer